Algorithms for accurate, validated and fast polynomial evaluation

DOI10.1007/BF03186531zbMath1184.65029MaRDI QIDQ849175

Stef Graillat, Philippe Langlois, Nicolas Louvet

Publication date: 25 February 2010

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jjiam/1265033778

zbMATH Keywords

numerical experimentsfloating-point arithmeticpolynomial evaluationcompensated algorithmerror-free transformationHorner algorithmIEEE-754

Mathematics Subject Classification ID

Related Items (15)

Accurate evaluation of a polynomial and its derivative in Bernstein form ⋮ On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots ⋮ Matrix representations for multi-degree B-splines ⋮ Reducing rounding errors and achieving Brouwer's law with Taylor series method ⋮ Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form ⋮ High-precision computation: mathematical physics and dynamics ⋮ Accurate quotient-difference algorithm: error analysis, improvements and applications ⋮ Evaluation schemes in the ring of quaternionic polynomials ⋮ Algorithm 954 ⋮ Compensated de Casteljau algorithm in \(K\) times the working precision ⋮ Accurate evaluation of a polynomial in Chebyshev form ⋮ Numerical validation of compensated algorithms with stochastic arithmetic ⋮ An accurate algorithm for evaluating rational functions ⋮ Accurate evaluation of polynomials in Legendre basis ⋮ PACF: a precision-adjustable computational framework for solving singular values

Uses Software

• mctoolbox
• LBNL
• XBLAS

Cites Work

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• More accuracy at fixed precision.
• A floating-point technique for extending the available precision
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Summation Part I: Faithful Rounding
• Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit
• Design, implementation and testing of extended and mixed precision BLAS
• Accurate Sum and Dot Product

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